🧮 algebra

1. El problema es resolver el sistema de ecuaciones por el método de sustitución: $$\begin{cases} x - y = 4 \\ x = 3y \end{cases}$$

1. Planteamos el problema: Comparar la proporción de azúcar respecto al cacao en dos recetas. 2. La fórmula para la proporción es: $$\text{Proporción} = \frac{\text{azúcar}}{\text{

1. **State the problem:** Solve the equation $2x + 5 = 3(x - 2)$. 2. **Write the formula and rules:** We will use the distributive property and properties of equality to isolate $x

1. **State the problem:** Solve the equation $$3(4 - x) = 6(x + 2)$$ for $x$. 2. **Rewrite the equation:** Distribute the constants on both sides:

1. **State the problem:** We are given the function $s(x) = \mu[\sin(2x) - 1]$ defined on the interval $[-\pi, \pi]$ and the inequality $s(x) < \frac{1}{2}$. We need to determine t

1. El problema pide resolver la expresión: $$(-c)^0 \cdot (-c) \cdot (-c)^{11} \cdot (-c)^{10} : (-c)^{22}$$. 2. Recordemos las propiedades de las potencias:

1. **Planteamiento del problema:** Calcular el valor de la expresión $$(-c)^\circ \cdot (-c) \cdot (-c)^{11} \cdot (-c)^{10} : (-c)^{22}$$. 2. **Reglas y fórmulas importantes:**

1. **State the problem:** Solve the system of linear equations: $$y = 0.5x + 4$$

1. **State the problem:** Solve the system of linear equations: $$-6x + y = 3$$

1. **Resuelve la ecuación** $\frac{1}{6} = \frac{x}{5}$ para encontrar $x$. 2. Usamos la propiedad de las proporciones: $$\frac{a}{b} = \frac{c}{d} \implies ad = bc$$

1. **Problem:** Calculate the value of expression a) from Bài 8: $$2^3 - \frac{5^3}{5^2} + 12 \cdot 2^2$$ 2. **Formula and rules:**

1. **Problem:** Calculate the value of expression a) from Bài 8: $$2^3 - \frac{5^3}{5^2} + 12 \cdot 2^2$$ 2. **Formula and rules:**

1. **State the problem:** We need to find the value of the composition of functions \( (p \circ q)(-2) \), where \( p(x) = 6x \) and \( q(x) = x + 4 \). 2. **Recall the definition

1. The problem asks to find the value of the composition of functions $(c \circ d)(4)$, where $c(x) = 2x$ and $d(x) = 6x$. 2. The composition of functions $(c \circ d)(x)$ means $c

1. **State the problem:** Simplify the expression $$\frac{\left(7^{-3}\right)^5^{-1}}{7^4 \cdot 7^{-5}} \cdot \frac{49^4}{49^{-5}}$$. 2. **Recall the rules:**

1. The problem is to calculate the value of $-0.2675$ per hour multiplied by 7 days. 2. We use the formula for multiplication of a rate by a time period: $$\text{Result} = \text{Ra

1. **State the problem:** Calculate the value of the expression $$\frac{1348000}{(1.06)^2}$$. 2. **Formula and rules:** This is a division problem where the denominator is a power

1. **State the problem:** Calculate the value of the expression $$\frac{1.348.00}{(1,06)^2}$$. 2. **Clarify notation:** The expression likely means $$\frac{1348.00}{(1.06)^2}$$ whe

1. **State the problem:** Find the zeros of the quadratic equation using the quadratic formula. 2. **Quadratic formula:**

1. **State the problem:** Simplify the algebraic expression $10a - 5a - 2 + a + 10a$. 2. **Identify like terms:** Like terms are terms that contain the same variable raised to the

1. Planteamos el problema: Simplificar la suma de fracciones \( \frac{7a^2 - 6a - 2}{10a^2} + \frac{a^2 + 3a - 1}{10a^2} \). 2. Observamos que ambas fracciones tienen el mismo deno